共查询到20条相似文献,搜索用时 31 毫秒
1.
Let and be polynomials with real zeros satisfying An?1 = Bn?1 = 0, and let Using the recently proved validity of the van der Waerden conjecture on permanents, some results on the real zeros of H(x) are obtained. These results are related to classical results on composite polynomials. 相似文献
2.
Let A denote a decomposable symmetric complex valued n-linear function on Cm. We prove , where · denotes the symmetric product and ? the tensor product. As a consequence we have per , where M is a positive semidefinite Hermitian matrix and per denotes the permanent function. A sufficient condition for equality in the matrix inequality is that M is a nonnegative diagonal matrix. 相似文献
3.
R.J Cook 《Journal of Number Theory》1983,17(1):80-92
Let k be an odd positive integer. Davenport and Lewis have shown that the equations with integer coefficients, have a nontrivial solution in integers x1,…, xN provided that Here it is shown that for any ? > 0 and k > k0(?) the equations have a nontrivial solution provided that 相似文献
4.
This paper considers canonical forms for the similarity action of Gl(n) on : , Those canonical forms are obtained as an application of a more general method to select canonical elements Mc in the orbits of a matrix group G acting on a set of matrices . We define a total order (?) on , different from the lexicographic order l? [0l?x ? x <0, but and consider normalized -elements with a minimal number of parameters: It is shown that the row and column echelon forms, the Jordan canonical form, and “nice” control canonical forms for reachable (A,B)-pairs have a homogeneous interpretation as such (?)-minimal orbit elements. Moreover new canonical forms for the general action (?) are determined via this method. 相似文献
5.
Let Ms, be the number of solutions of the equation in the finite field GF(p). For a prime p ≡ 1(mod 3), , , and . Here d is uniquely determined by . 相似文献
6.
If f is a positive function on (0, ∞) which is monotone of order n for every n in the sense of Löwner and if Φ1 and Φ2 are concave maps among positive definite matrices, then the following map involving tensor products: is proved to be concave. If Φ1 is affine, it is proved without use of positivity that the map is convex. These yield the concavity of the map (0<p?1) (Lieb's theorem) and the convexity of the map (0<p?1), as well as the convexity of the map .These concavity and convexity theorems are then applied to obtain unusual estimates, from above and below, for Hadamard products of positive definite matrices. 相似文献
7.
Ludwig Arnold 《Linear algebra and its applications》1976,13(3):185-199
It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let An=(aij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ(n)}1?k?n its eigenvalues, and {uk(n)}1?k?n the corresponding (orthonormalized column) eigenvectors. Let , put (bookeeping function for the length of the projections of the new row v1n of An onto the eigenvectors of the preceding matrix An?1), and let finally (empirical distribution function of the eigenvalues of . Suppose (i) , (ii) limnXn(t)=Ct(0<C<∞,0?t?1). Then ,where W is absolutely continuous with (semicircle) density 相似文献
8.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
9.
A.M Fink 《Journal of Mathematical Analysis and Applications》1982,90(1):251-258
Presented in this report are two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of the following theorem of V. M. Olovyani?nikov: LetNn (n ? 2) be the class of functionsg(x) such thatg(x), g′(x),…, g(n)(x) are ? 0, bounded, and nondecreasing on the half-line ?∞ < x ? 0. A special element ofNnis. Ifg(x) ∈ Nnis such that, thenfor
1
. Moreover, if we have equality in (1) for some value of v, then we have there equality for all v, and this happens only if in (?∞, 0].The second application gives sufficient conditions for the differentiability of asymptotic expansions (Theorem 4). 相似文献
10.
George Phillip Barker 《Linear algebra and its applications》1977,16(3):233-235
Let A be an n×n matrix with complex entries. A necessary and sufficient condition is established for the existence of a Hermitian solution H to the equations . 相似文献
11.
An n-tournament is a complete labelled digraph on n vertices without loops or multiple arcs. A tournament's score sequence is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The number Sn of distinct score sequences arising from all possible n-tournaments, as well as certain generalizations are investigated. A lower bound of the form (C1 a constant) and an upper bound of the form are proved. A q-extension of the Catalan numbers is defined. It is conjectured that all coefficients in the polynomial Cn(q) are at most . It is shown that if this conjecture is true, then 相似文献
12.
13.
Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献
14.
Thomas H. Pate 《Linear algebra and its applications》1976,14(3):285-292
Suppose each of m, n, and k is a positive integer, k ? n, A is a (real-valued) symmetric n-linear function on Em, and B is a k-linear symmetric function on Em. The tensor and symmetric products of A and B are denoted, respectively, by A ?B and A?B. The identity is proven by Neuberger in [1]. An immediate consequence of this identity is the inequality In this paper a necessary and sufficient condition for is given. It is also shown that under certain conditions the inequality can be considerably improved. This improvement results from an analysis of the terms 6A?qB6, 1?q?n, appearing in the identity. 相似文献
15.
John R Dickerson Paul A Erickson 《Journal of Mathematical Analysis and Applications》1974,47(3):513-519
The behavior of an infinite sequence of ordinary differential equations of the form: , , where Xn(t) is a vector valued function of R+, is studied in spaces of infinite sequences of vectors. In particular, sufficient conditions for asymptotic stability of this sequence of linear equations are established and applied to the stability analysis of a string of vehicles with a simple form of automatic control. 相似文献
16.
This paper is a study of the distribution of eigenvalues of various classes of operators. In Section 1 we prove that the eigenvalues (λn(T)) of a p-absolutely summing operator, p ? 2, satisfy This solves a problem of A. Pietsch. We give applications of this to integral operators in Lp-spaces, weakly singular operators, and matrix inequalities.In Section 2 we introduce the quasinormed ideal Π2(n), P = (p1, …, pn) and show that for T ∈ Π2(n), 2 = (2, …, 2) ∈ Nn, the eigenvalues of T satisfy More generally, we show that for T ∈ Πp(n), P = (p1, …, pn), pi ? 2, the eigenvalues are absolutely p-summable, We also consider the distribution of eigenvalues of p-nuclear operators on Lr-spaces.In Section 3 we prove the Banach space analog of the classical Weyl inequality, namely , 0 < p < ∞, where αn denotes the Kolmogoroff, Gelfand of approximation numbers of the operator T. This solves a problem of Markus-Macaev.Finally we prove that Hilbert space is (isomorphically) the only Banach space X with the property that nuclear operators on X have absolutely summable eigenvalues. Using this result we show that if the nuclear operators on X are of type l1 then X must be a Hilbert space. 相似文献
17.
L.B Richmond 《Journal of Number Theory》1976,8(4):390-396
Asymptotic results are obtained for pA(k)(n), the kth difference of the function pA(n) which is the number of partitions of n into integers from A. Under certain restrictions on A it is shown that thereby verifying for these A a conjecture of Bateman and Erdös. 相似文献
18.
M Jungerman 《Journal of Combinatorial Theory, Series B》1979,26(2):154-158
The nonorientable genus of K4(n) is shown to satisfy: , . 相似文献
19.
Raul Cordovil 《Journal of Combinatorial Theory, Series B》1983,34(2):209-223
A natural sufficient condition for a finite family of single element extensions of a matroid to be compatible is given. Characterizations of all the finite extensions N of a matroid M(E) are given for which the rank function satisfies or equivalently the closure operator satisfies . The single element extensions and the principal extensions are examples of such matroids. The notion of a sheaf of flats of M. Las Vergnas is used in the proof of a new necessary and sufficient condition for two single element extensions of a matroid to be compatible. An initial announcement of part of these results appeared in R. Cordovil (C. R. Acad. Sci. Paris. A284 (1977), 1249–1252). 相似文献
20.